几何约束的改进弹性体网格变形方法研究及应用
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摘要
针对现有弹性体网格变形方法无法有效抑制网格单元出现"负体积"和过度畸变等问题,引入体积弹性模量约束和挤压弹性模量约束,提出一种基于几何约束的改进弹性体法。借助Patrick网格质量参数,选取三维长方体边界在旋转、平移和伸展变形三种方式下的大幅度运动,对比研究引入几何约束后的改进效果。仿真计算二维NACA0012翼型的俯仰振荡和三维伸缩翼变形过程的气动特性,结果表明:基于几何约束的改进弹性体法显著提高了变形网格的鲁棒性,尤其在大变形时能够有效约束较差网格单元,改善经典方法存在的问题,可为非定常流场问题的求解提供有力支撑。
Aimed at the problem that the current elasticity-based mesh deformation method always cannot control some poor elements suffering"negative volume"and extreme distortion,the volume and the extruding constraints on modulus of elasticity were introduced to solve above shortages and a modified elasticity-based method based on these geometry constraints was presented. Combined with Patrick mesh quality measure,the differences between the modified method and the classical method were fully analyzed by testing a 3D cubic model with three types of motion or deformation in wide-range,such as rotation,translation,and stretch. The modified method was applied to simulate the plunging motion of NACA0012 airfoil and stretching deformation of wing. Results show this modified method can improve the robustness of elasticity-based method by constraining poor elements in wide-range of motion or deformation,thus providing a better support for solving the unsteady flow problems.
Aimed at the problem that the current elasticity-based mesh deformation method always cannot control some poor elements suffering"negative volume"and extreme distortion,the volume and the extruding constraints on modulus of elasticity were introduced to solve above shortages and a modified elasticity-based method based on these geometry constraints was presented. Combined with Patrick mesh quality measure,the differences between the modified method and the classical method were fully analyzed by testing a 3D cubic model with three types of motion or deformation in wide-range,such as rotation,translation,and stretch. The modified method was applied to simulate the plunging motion of NACA0012 airfoil and stretching deformation of wing. Results show this modified method can improve the robustness of elasticity-based method by constraining poor elements in wide-range of motion or deformation,thus providing a better support for solving the unsteady flow problems.
引文
[1]周璇,李水乡,孙树立,等.非结构网格变形方法研究进展[J].力学进展,2011,41(5):547-561.ZHOU Xuan,LI Shuixiang,SUN Shuli,et al.Advances in the research on unstructured mesh deformation[J].Advances in Mechanics,2011,41(5):547-561.(in Chinese)
[2]张斌.弹性体动网格方法改进及在高超声速体襟翼非定常仿真中的初步应用[D].长沙:国防科技大学,2015.ZHANG Bin.Research on the improvement in elasticity-based dynamic mesh method and preliminary application for unsteady flow simulation of body flap in hypersonic vehicle[D].Changsha:National University of Defense Technology,2015.(in Chinese)
[3]Tezduyar E T.Stabilized finite element formulations for incompressible flow computations[J].Advances in Applied Mechanics,1992,28:1-44.
[4]Stein K,Tezduyar T,Benney R.Mesh moving techniques for fluid-structure interactions with large displacements[J].Journal of Applied Mechanics,2003,70(1):58-63.
[5]Abgrall R,Dobrzynski C,Froehly A.A method for computing curved meshes via the linear elasticity analogy,application to fluid dynamics problems[J].International Journal for Numerical Methods in Fluids,2014,76(4):246-266.
[6]Albring T,Sagebaumy M,Gauger N R.Efficient aerodynamic design using the discrete adjoint method in SU2[C]//Proceedings of 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference,2016.
[7]张斌,杨涛,丰志伟,等.非结构弹性体动网格方法应用策略及改进[J].航空动力学报,2017,32(3):648-656.ZHANG Bin,YANG Tao,FENG Zhiwei,et al.Application strategy and improvement of unstructured dynamic grid method based on elasticity analogy[J].Journal of Aerospace Power,2017,32(3):648-656.(in Chinese)
[8]谭伟伟,刘峰博,张一帆.基于线性弹性体的网格变形方法研究[J].航空计算技术,2017,47(2):37-40.TAN Weiwei,LIU Fengbo,ZHANG Yifan.Study on linear elastic solid based grid deformation method[J].Aeronautical Computing Technique,2017,47(2):37-40.(in Chinese)
[9]仲继泽,徐自力.基于动网格降阶算法的机翼颤振边界预测[J].振动与冲击,2017,36(4):185-191.ZHONG Jize,XU Zili.Wing flutter prediction using a reduced dynamic mesh method[J].Journal of Vibration and Shock,2017,36(4):185-191.(in Chinese)
[10]张伟伟,高传强,叶正寅.气动弹性计算中网格变形方法研究进展[J].航空学报,2014,35(2):303-319.ZHANG Weiwei,GAO Chuanqiang,YE Zhengyin.Research progress on mesh deformation method in computational aeroelasticity[J].Acta Aeronautica et Astronautica Sinica,2014,35(2):303-319.(in Chinese)
[11]L9hner R.Applied computational fluid dynamics techniques:an introduction based on finite element methods[M].2nd ed.USA:John Wiley&Sons,2008.
[12]刘君,白晓征,郭正.非结构动网格计算方法---及其在包含运动界面的流场模拟中的应用[M].长沙:国防科技大学出版社,2009.LIU Jun,BAI Xiaozheng,GUO Zheng.Unstructured grid moving method and its application for the simulation of flow with moving interface[M].Changsha:National University of Defence Technology Press,2009.(in Chinese)
[13]高传强,张伟伟,蒋跃文,等.两种典型非结构网格变形方法特性对比研究[J].航空工程进展,2014,5(2):212-219.GAO Chuanqiang,ZHANG Weiwei,JIANG Yuewen,et al.A comparative study on two typical unstructured grid deformation methods[J].Advances in Aeronautical Science and Engineering,2014,5(2):212-219.(in Chinese)
[14]Palacios F,Economon T D,Aranake A,et al.Stanford university unstructured(SU2):open-source analysis and design technology for turbulent flows[C]//Proceedings of52nd Aerospace Sciences Meeting,2014.
[15]李媛,康顺.振荡翼型非定常气动特性数值模拟[J].工程热物理学报,2012,33(9):1505-1508.LI Yuan,KANG Shun.Numerical simulation of oscillating airfoil unsteady aerodynamic performance[J].Journal of Engineering and Thermophysics,2012,33(9):1505-1508.(in Chinese)
[2]张斌.弹性体动网格方法改进及在高超声速体襟翼非定常仿真中的初步应用[D].长沙:国防科技大学,2015.ZHANG Bin.Research on the improvement in elasticity-based dynamic mesh method and preliminary application for unsteady flow simulation of body flap in hypersonic vehicle[D].Changsha:National University of Defense Technology,2015.(in Chinese)
[3]Tezduyar E T.Stabilized finite element formulations for incompressible flow computations[J].Advances in Applied Mechanics,1992,28:1-44.
[4]Stein K,Tezduyar T,Benney R.Mesh moving techniques for fluid-structure interactions with large displacements[J].Journal of Applied Mechanics,2003,70(1):58-63.
[5]Abgrall R,Dobrzynski C,Froehly A.A method for computing curved meshes via the linear elasticity analogy,application to fluid dynamics problems[J].International Journal for Numerical Methods in Fluids,2014,76(4):246-266.
[6]Albring T,Sagebaumy M,Gauger N R.Efficient aerodynamic design using the discrete adjoint method in SU2[C]//Proceedings of 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference,2016.
[7]张斌,杨涛,丰志伟,等.非结构弹性体动网格方法应用策略及改进[J].航空动力学报,2017,32(3):648-656.ZHANG Bin,YANG Tao,FENG Zhiwei,et al.Application strategy and improvement of unstructured dynamic grid method based on elasticity analogy[J].Journal of Aerospace Power,2017,32(3):648-656.(in Chinese)
[8]谭伟伟,刘峰博,张一帆.基于线性弹性体的网格变形方法研究[J].航空计算技术,2017,47(2):37-40.TAN Weiwei,LIU Fengbo,ZHANG Yifan.Study on linear elastic solid based grid deformation method[J].Aeronautical Computing Technique,2017,47(2):37-40.(in Chinese)
[9]仲继泽,徐自力.基于动网格降阶算法的机翼颤振边界预测[J].振动与冲击,2017,36(4):185-191.ZHONG Jize,XU Zili.Wing flutter prediction using a reduced dynamic mesh method[J].Journal of Vibration and Shock,2017,36(4):185-191.(in Chinese)
[10]张伟伟,高传强,叶正寅.气动弹性计算中网格变形方法研究进展[J].航空学报,2014,35(2):303-319.ZHANG Weiwei,GAO Chuanqiang,YE Zhengyin.Research progress on mesh deformation method in computational aeroelasticity[J].Acta Aeronautica et Astronautica Sinica,2014,35(2):303-319.(in Chinese)
[11]L9hner R.Applied computational fluid dynamics techniques:an introduction based on finite element methods[M].2nd ed.USA:John Wiley&Sons,2008.
[12]刘君,白晓征,郭正.非结构动网格计算方法---及其在包含运动界面的流场模拟中的应用[M].长沙:国防科技大学出版社,2009.LIU Jun,BAI Xiaozheng,GUO Zheng.Unstructured grid moving method and its application for the simulation of flow with moving interface[M].Changsha:National University of Defence Technology Press,2009.(in Chinese)
[13]高传强,张伟伟,蒋跃文,等.两种典型非结构网格变形方法特性对比研究[J].航空工程进展,2014,5(2):212-219.GAO Chuanqiang,ZHANG Weiwei,JIANG Yuewen,et al.A comparative study on two typical unstructured grid deformation methods[J].Advances in Aeronautical Science and Engineering,2014,5(2):212-219.(in Chinese)
[14]Palacios F,Economon T D,Aranake A,et al.Stanford university unstructured(SU2):open-source analysis and design technology for turbulent flows[C]//Proceedings of52nd Aerospace Sciences Meeting,2014.
[15]李媛,康顺.振荡翼型非定常气动特性数值模拟[J].工程热物理学报,2012,33(9):1505-1508.LI Yuan,KANG Shun.Numerical simulation of oscillating airfoil unsteady aerodynamic performance[J].Journal of Engineering and Thermophysics,2012,33(9):1505-1508.(in Chinese)